Bowker was born in Shawford, Hampshire, England. On stage from childhood, she first attracted international attention as the star of The Adventures of Black Beauty, a 1972 TV series which was a "continuation" of the book.
She also starred as Clare of Assisi in Franco Zeffirelli's Brother Sun, Sister Moon, also from 1972. Her other well-known film appearances are as Princess Andromeda in the 1981 Ray Harryhausen film, Clash of the Titans and as Lady Olivia Lilburn in Alan Bridges' The Shooting Party (1985).
She is married to Harry Meacher.